Closure relations for the shear stress in two-fluid models for core-annular flow

The exact solution for laminar core-annular flow (CAF) in inclined pipes is used to derive new closure relations for the wall and interfacial shear stresses. These are incorporated in a two-fluid model for CAF. With these closure relations, the two-fluid model yields the exact solution for the hold-up and pressure drop in case of laminar horizontal or inclined CAF. It is shown that multiple solutions can be obtained in upward or downward inclined systems. The multiple solution regions are identified in terms of the controlling dimensionless parameters. The predictions of the two-fluid model for laminar and turbulent CAFs are tested against experimental data available from the literature for oil-water systems. The good comparison suggests the two-fluid model as convenient tool for evaluating the pressure drop and holdup in CAF.